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Artificial Intelligence Review

, Volume 38, Issue 2, pp 85–95 | Cite as

A tutorial on variational Bayesian inference

  • Charles W. Fox
  • Stephen J. Roberts
Article

Abstract

This tutorial describes the mean-field variational Bayesian approximation to inference in graphical models, using modern machine learning terminology rather than statistical physics concepts. It begins by seeking to find an approximate mean-field distribution close to the target joint in the KL-divergence sense. It then derives local node updates and reviews the recent Variational Message Passing framework.

Keywords

Variational Bayes Mean-field Tutorial 

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References

  1. Attias H (2000) A variational Bayesian framework for graphical models. In: Advances in neural information processing systems. MIT PressGoogle Scholar
  2. Bernardo JM, Smith AFM (2000) Bayesian theory. Wiley, LondonzbMATHGoogle Scholar
  3. Bishop CM, Winn JM, Spiegelhalter D (2002) VIBES: a variational inference engine for Bayesian networks. In: Advances in neural information processing systemsGoogle Scholar
  4. Winn J, Bishop C (2005) Variational message passing. J Mach Learn Res 6: 661–694MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Adaptive Behaviour Research GroupUniversity of SheffieldSheffieldUK
  2. 2.Pattern Analysis and Machine Learning Research Group, Department of Engineering ScienceUniversity of OxfordOxfordUK

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